Optical waveguide devices used as optical modulators in recent optical communication systems include a substrate having an electro-optic crystal such as LiTaO2 or LiNbO3 (LN). The optical waveguide device can change a refractive index of an optical waveguide formed in the substrate by causing an electric field to act on the optical waveguide. In the optical waveguide device, for example, a Mach-Zehnder (MZ) type structure is well known as an interference structure that uses an optical waveguide formed in an electro-optic crystal substrate. A Mach-Zehnder type optical interference structure that uses the optical waveguide includes an input waveguide section, a waveguide section including two parallel waveguides in which light input to the input waveguide section is branched and propagated, and an output waveguide section that combines the branched light having propagated in the waveguide section. Moreover an electrode that causes an electric field to act on the parallel waveguides in the waveguide section is formed above the substrate via a buffer layer such as SiO2.
As the electrode of the optical waveguide device including the Mach-Zehnder type optical interference structure that uses the optical waveguide, a coplanar electrode provided on the waveguide section in the form of a signal electrode and a ground electrode may be adopted. Furthermore in the case in which the electro-optic crystal substrate is a Z-cut substrate, the signal electrode and the ground electrode are formed respectively so as to have a portion overlapping on the parallel waveguides in the waveguide section. Moreover, the signal electrode and the ground electrode are formed in a configuration of a traveling-wave electrode with one end of the signal electrode being grounded via a resistor and terminated, corresponding to higher frequencies of signal light to be modulated. For example, a microwave high-frequency electric signal is applied to the other end of the signal electrode in the form of the traveling-wave electrode.
A Mach-Zehnder type optical modulator that uses the optical waveguide adopts a structure in which many waveguide sections are integrated on a single substrate, corresponding to diversification of an optical modulation system, such as for example, Return-to-Zero (RZ) modulation, multilevel modulation, and polarization multiplexing modulation. As one example, FIG. 10 illustrates an optical waveguide device in which four waveguide sections are formed in a substrate.
In FIG. 10, an optical waveguide device 1 includes an optical waveguide 3 extending in a length direction of an LN substrate 2. The optical waveguide 3 is formed in the Z-cut LN substrate 2 by a process of patterning and thermally diffusing a metal film such as Ti, or by a process of subjecting the metal film to proton exchange in benzoic acid after patterning. The optical waveguide 3 includes three parts, that is; an input waveguide section 3a for inputting light, four waveguide sections 3b for branching and propagating light input to the input waveguide section 3a, and an output waveguide section 3c for combining the branched lights having propagated in the waveguide section 3b. That is, the four waveguide sections 3b are connected in parallel between the input waveguide section 3a formed at one end of the LN substrate 2 and the output waveguide section 3c formed at the other end of the LN substrate 2.
In the four waveguide sections 3b, each of the waveguide sections 3b are formed by two parallel waveguides. Moreover a signal electrode 4 and a ground electrode 5 for causing an electric field to act, are provided for each waveguide section 3b, with a buffer layer 2a interposed therebetween (refer to FIG. 11). As illustrated in FIG. 10, the ground electrode 5 is formed wider than the signal electrode 4 in a cross direction D2 intersecting an extension direction D1 of the waveguide section 3b, in order to obtain excellent high frequency characteristics.
The ground electrode 5 illustrated in FIG. 10 has a portion divided into a narrow portion 5a having a narrow electrode width and a wide portion 5b having a wide electrode width in the cross direction D2, and the narrow portion 5a overlaps on one of the waveguides of the waveguide section 3b. The narrow portion 5a and the wide portion 5b are connected to each other by bridge portions 5c provided at a predetermined pitch in the extension direction D1. The reason why the ground electrode 5 is divided in the cross direction D2 as illustrated in FIG. 10 is to suppress a stress applied to the waveguide section 3b under the ground electrode 5 resulting from a difference in thermal expansion between the ground electrode 5 and the LN substrate 2.
When a stress is applied to the waveguide section 3b due to the difference in thermal expansion, it affects the refractive index of the optical waveguide at a portion where the stress is applied, and a variation occurs in a voltage that turns off an output light output from the output waveguide section 3c. With respect to this voltage variation, a control is effective that separately applies a bias voltage (DC) to the electrode, and adjusts the bias voltage while monitoring the output light, to thereby optimize an operating point of the optical modulator. However in this case there is a problem in that the drive voltage increases. To solve this problem, a portion positioned on the waveguide section 3b is made the narrow portion 5a by dividing the wide ground electrode 5, to weaken the stress applied to the optical waveguide, thereby suppressing operating point variations due to temperature fluctuations as much as possible. On the other hand, with regard to the high frequency characteristics of the electrode, the bridge portion 5c is formed to connect the narrow portion 5a and the wide portion 5b to ensure a sufficient grounded state, thereby maintaining the high frequency characteristics. Japanese Unexamined Patent Publication No. 2006-084537 (Patent Document 1) discloses the configuration of dividing the ground electrode.
The ground-electrode dividing structure disclosed in Patent Document 1 is for equalizing the stress due to the electrode in the cross direction intersecting the extension direction of the waveguide section, by reducing the stress applied to the optical waveguide from the wide ground electrode down to a similar level to the stress due to the thin signal electrode. However as illustrated in FIG. 10, the LN substrate 2 of the optical waveguide device 1 is supported by a support member 6 in a casing in which the optical waveguide device 1 is installed. Therefore, there is a stress applied to the lower surface of the LN substrate 2 from the support member 6, other than the stress applied to the upper surface of the LN substrate 2 from the ground electrode 5. The support member 6 is a part of the casing or a part separate from the casing, and is made of metal such as SUS, and there is a difference in thermal expansion between the LN substrate 2 and the support member 6. Because the LN substrate 2 is fixed to the support member 6 by using an adhesive or the like, the LN substrate 2 also receives a stress from the lower surface of the substrate due to the difference in thermal expansion between the LN substrate 2 and the support member 6. The stress applied by the support member 6 from the lower surface of the LN substrate 2 changes in magnitude in the cross direction D2. The stress applied by the support member 6 with respect to the four parallel waveguides 3b arranged in the width direction of the LN substrate 2 in FIG. 10 will be explained with reference to FIG. 11.
FIG. 11 is a cross-section along line A-A in FIG. 10, of the optical waveguide device 1 fixed to the support member 6. The coefficient of thermal expansion of the support member 6 is smaller than that of the LN substrate 2, and the stress applied from the support member 6 to the LN substrate 2 due to a difference in thermal expansion attributable to the difference in coefficient of thermal expansion, becomes stronger with approach to the sides of the LN substrate 2. Consequently, when as illustrated in FIG. 10 and FIG. 11, the four waveguide sections 3b are arranged in the LN substrate 2 substantially symmetrically in the width direction of the substrate to equalize the stress due to the electrodes 4 and 5 in the width direction of the substrate, as shown in FIG. 11, the distribution of the stress applied from the support member 6 to the LN substrate 2 in the cross direction D2 exhibits characteristics such that the distribution center substantially coincides with the widthwise center of the substrate and the stress distribution becomes gradually stronger from the center of stress distribution toward the sides of the substrate.
Attributable to the stress due to the support member 6 illustrated in FIG. 11, with regard to two waveguide sections 3b-in of the four waveguide sections 3b, that are closer to the center of stress distribution, a stress difference X generated between each of the two waveguides constituting the waveguide sections 3b-in becomes small. On the other hand, with regard to two waveguide sections 3b-out farther from the center of stress distribution, a stress difference Y generated between each of the two waveguides constituting the waveguide sections 3b-out becomes large. That is, in the cross direction D2, a difference in stress characteristics occurs between the plurality of waveguide sections 3b. When a stress difference generated between two waveguides increases in one waveguide section 3b, the operating point variation due to temperature fluctuation increases. Therefore a difference occurs in the operating point variation corresponding to the position in the substrate where the waveguide section 3b is formed.
FIG. 12 illustrates operating point variation due to the position in the substrate of the waveguide section 3b illustrated in FIG. 11. In FIG. 12, the Y axis shows voltage variation (V) of the operating point accompanying a temperature fluctuation, with an operating point voltage in the normal state designated as “1”. Moreover, the X axis shows distance (μm) from the widthwise center of the substrate. In the case of FIG. 11, because the widthwise center of the substrate substantially coincides with the center of stress distribution as described above, the widthwise center of the substrate on the X axis in FIG. 12 is the center of stress distribution.
The respective points in FIG. 12 are obtained by plotting variation in operating point voltage in the four waveguide sections 3b at the time of changing the temperature, corresponding to distance on the X axis. As illustrated in FIG. 12, in the waveguide sections 3b-in closer to the center of stress distribution in the cross direction D2, the operating point voltage varies only by about 1V in absolute value, due to temperature fluctuations. On the other hand, in the waveguide sections 3b-out farther from the center of stress distribution in the cross direction D2, the operating point voltage varies by about 3V in absolute value, due to temperature fluctuations. The reason why the sign (±) of the operating point variations is different between the left and right positions is due to whether the ground electrode 5 is provided with respect to the inside waveguide or with respect to the outside waveguide, of the two waveguides, in one waveguide section 3b. 
To prevent such a difference in the operating point variation corresponding to the position of the waveguide section in the substrate, there may be considered a method of enlarging the width of the LN substrate 2, or narrowing down a mutual interval between the waveguide sections 3b. However, if the substrate width is enlarged, there is a problem in that the number of substrates that can be cut out from a wafer decreases. Moreover if the mutual interval is narrowed down there is a problem in that crosstalk increases. Therefore, currently there is no satisfactory solution.